Question

Three particles $P, Q$ and $R$ are at rest at the vertices of an equilateral triangle of side $s$ . Each of the particles starts moving with constant speed $v \,ms^{-1}. P$ is moving along $PQ, Q$ along $QR$ and $R$ along $RP$ . The particles will meet each other at time $t$ given by

• A. $\frac{s}{v}$
• B. $\frac{3s}{v}$
• C. $\frac{3s}{2v}$
• D. $\frac{2s}{3v}$

Answer 1

Answer: (D)

$\frac{2s}{3v}$

Answer 2

The velocity component towards centroid $O$ of
triangle $= vcos \,\theta$
$= v \, cos \,30^{\circ} = \frac{\sqrt{3}}{2} v$
Distance $P O = - \frac{2}{3}$ of altitude
$= \frac{2}{3} \times \frac{\sqrt{3}}{2} s = \frac{1}{\sqrt{3}} s$
$\Rightarrow$ Time $= \frac {\text{Distance}}{\text{Speed}}$
$= \frac{\frac{1}{\sqrt{3}} s}{\frac{\sqrt{3}}{2} v}$
$= \frac{2}{3} \cdot \frac{s}{v}$